Molecular mobility fractal characteristics

The use of fractal analysis makes it possible to relate molecular parameters to characteristics of supermolecular structure of polymers. Figure 11.12 illustrates the linear correlation between D and df [dj was estimated from Equation (11.27)] for epoxy polymers. When the molecular mobility is suppressed (D = 1), the structure of the polymer has the fractal dimension df = 2.5, which corresponds to p. = 0.25. The given value of the Poisson coefficient corresponds to the boundary of ideally brittle structure at p< 0.25, the polymer is collapsed without viscoelastic or plastic dissipation of energy [3]. This is fnlly consistent with the Kansch conclnsion [117] stating that any increase in the molecular mobility enhances dissipation of the mechanical energy supplied from the outside and, as a conseqnence, increases plasticity of the polymer. When D = 2 the df value is equal to 3, which corresponds to p = 0.5, typical of the rubbery state. 

Description of Molecular Mobility Using Fractal Characteristics... 

Hence, the adduced above results shown that the main factor, influencing on molecular mobility level in HDPE noncrystalline regions, is these regions structure, characterized by fractal dimension or relative fraction of local order regions (clusters) (p j. Definite influence is exercised by molecular characteristics, especially if to take into account, that between and (p, on the one hand, and S and C, on the other hand, the close intercommunication exists (see, for the example, the Eqs. (1.11) and (1.12)). As consequence, the equations using, taking into account their structural state, will be correct for polymers dimension estimation [38]. 

As it was shown earlier [11, 15], the fractal dimension of a chain part between chemical crosslinking nodes is characteristic of its molecular mobility and changes within strictly appointed limits 1 < < 2. A number of methods for the estimation... 

In the present section a number of modern physical concepts for the description of the structure of crosslinked polymers is used the thermodynamic concept, the cluster model of amorphous state structure of polymers, fractal analysis, irreversible aggregation models and the thermal cluster model. Within the frameworks of the thermodynamic approach the interconnection of structural and molecular characteristics of crosslinked polymers with disorder parameter 8 is considered [69]. According to the concept [69] the indicated parameter, connected with the thermal mobility of molecules near the melting temperature, is expressed by Formula 1.28. Since p. is given by Equation 1.29 then Relationship 1.30 can be received from combination of Equations 1.28 and 1.29. 

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